A comprehensive look at enhancing system efficiency highlights diverse approaches, from foundational compiler techniques to advanced AI-driven cloud management. One exploration delves into the Integer Set Library (ISL), a critical C library for polyhedral optimization. This detailed primer explains ISL's core concepts, data structures, and API for analyzing and optimizing loop nests and memory layouts, essential for sophisticated compiler optimization and code generation. Complementing this, original research from Google unveils LAVA, an innovative AI-powered system revolutionizing cloud data center resource allocation. LAVA continuously re-predicts virtual machine lifetimes and employs algorithms like NILAS, LAVA, and LARS to optimize VM placement, minimize fragmentation, and reduce migrations. In production, NILAS has significantly improved resource efficiency, marking a new standard for cloud operations.